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The sine-Gordon equation in toroidal magnetic-fusion experiments

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Abstract.

This paper presents a new nonlinear model which describes localized magnetohydrodynamic (MHD) modes in reversed-field pinch (RFP) experiments. To date, nearly all experimental and theoretical work in this area has relied on the use of Fourier decomposition of spatial variations as a function of time. Moreover, due to the complexity of this nonlinear problem, previous work has been restricted to the analysis of a relatively small number of modes. In contrast, the model studied in this paper, based on the damped-driven sine-Gordon (DDSG) equation, addresses the full nonlinearity, does not rely on Fourier decomposition, and does not require the range of the nonlinearity to be small. A specific consequence of working with the full nonlinearity is the existence of solitary waves in dispersive media. These solitary waves, a key part of the model, are used to describe the so-called slinky mode propagating in the plasma. A remarkable resemblance is seen between the waveforms obtained from experiments and the mathematical predictions of the new model.

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  1. Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, WI, 53706, USA

    J. L. Shohet

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Shohet, J. The sine-Gordon equation in toroidal magnetic-fusion experiments. Eur. Phys. J. Spec. Top. 147, 191–207 (2007). https://doi.org/10.1140/epjst/e2007-00209-5

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